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. 2005 Oct;48(5):400-8.

What is so odd about odds?

Bernard Montreuil  1 , Yves Bendavid, James Brophy
Affiliations

What is so odd about odds?

Bernard Montreuil et al. Can J Surg. 2005 Oct.

Abstract
in English, French

In clinical studies, the relative likelihood of an event occurring between 2 groups is often expressed as the risk ratio (RR) or the odds ratio (OR). The RR is an intuitive parameter that is relatively easy to interpret. Quantitative interpretation of an OR is much more difficult and is often incorrectly equated to that of an RR. The problem is that OR may differ substantially from RR, especially when the outcome of interest is common in the study population. This article explains and clarifies controversial issues surrounding the use and interpretation of the OR. Theoretical concepts relating to ORs are illustrated by examples from the surgical literature. By reviewing articles from 5 surgical journals over a 5-year period, we show that the OR is often presented and misinterpreted as equivalent to the RR. When the discrepancy is large, using OR uncritically as an estimate of RR will strongly bias inferences about treatment effect or cause of disease by amplifying the apparent strength of an association between an exposure and an outcome.

Dans les études cliniques, la probabilité relative d'occurrence d'un événement entre deux groupes est souvent exprimée sous forme de risque relatif (RR) ou de coefficient de probabilité (CP). Le RR est un paramètre intuitif relativement facile à interpréter. L'interprétation quantitative d'un CP est beaucoup plus difficile et on établit souvent à tort une équivalence avec celle d'un RR. Le problème, c'est que le CP peut différer considérablement du RR, particulièrement lorsque le résultat d'intérêt est commun dans la population à l'étude. Cet article explique et clarifie les enjeux controversés qui entourent l'utilisation et l'interprétation du CP. On illustre par des exemples tirés des documents sur la chirurgie les concepts reliés au CP. En critiquant des articles de cinq journaux chirurgicaux publiés sur une période de cinq ans, nous montrons que le CP est souvent présenté et interprété à tort comme l'équivalent du RR. Lorsque l'écart est important, l'utilisation du CP qu'on a critiqué comme estimation du RR biaisera fortement les déductions au sujet de l'effet du traitement ou de la cause d'une maladie en amplifiant la solidité apparente d'un lien entre une exposition et un résultat.

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Figures

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FIG. 1. The relationship between relative risk (RR) and odds ratio (OR) by incidence of the outcome among unexposed (P0) people. RR = OR/[(1– P0) + (P0 хOR)].
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FIG. 2. Estimated relative risk (RR) compared with odds ratio (OR) for all articles in which the incidence of the outcome among unexposed (P0) people was available.
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FIG. 3. The relationship between NNT calculated from an odds ratio (OR) and an estimated relative risk (RR) by incidence of the outcome among unexposed (P0) people. OR from 0.1 to 1. RR = OR/[(1– P0) + (P0 хOR)]. NNT (calculated from OR) = 1/[P0 – (OR хP0)]. NNT (calculated from RR) = 1/[P0 – (RR хP0)].
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